1. Field of the Invention
The present invention relates to a system of predicting an output result in response to unknown input data using a layered neural network, and more specifically to a learning method operated through a layered neural network for learning data including the rate of change of data inputted in time series.
2. Description of the Related Art
In a learning process performed using a layered neural network comprising an input layer, one or more intermediate or hidden layers, and an output layer, the steps of (1) applying input data, (2) outputting a result of a neural network, (3) presenting a correct answer, (4) calculating an error between the output result and the correct answer, and (5) adjusting the weight of each connection to minimize the error are repeatedly performed until the error can be sufficiently minimized. In such a learning method, a neural network can gradually reach and output a desired answer. That is, when a learning process is completed, the neural network stores a correct relationship value between an input and an output by successfully adjusting the weight of a connection.
Conventionally, unprocessed data are applied as learning data to a neural network. FIG. 1 shows an example of such learning data. It shows the data with nine black dots on the line represented by the function Y =1-X. A value of X for the black dots is applied to a neuron in the input layer. Then, a learning process starts to minimize the difference between an output of a neuron in the output layer and the value of Y.
FIG. 2 shows recognition results obtained after the neural network has learned only a part of nine-dot data shown in FIG. 1. It shows the recognition results of the values of Y for the three dots where the values of X are 0.1 through 0.3 after the neural network has learned the data of six dots where the values of X are 0.1 through 0.6. In this case, the average value of the resultant errors is 0.058.
FIG. 3 shows a recognition result after the neural network has learned the data shown in FIG. 1, that is, all the nine-dot data. In FIG. 3, the neural network learns the same data as those shown in FIG. 2, but it outputs an average error value 0.024, which is much better than that shown in FIG. 2 where only partial data were learned.
Thus, in a learning process through a layered neural network, it is desirable to provide all the predictable patterns as learning data. However, it is actually impossible to prepare all patterns. Especially, in a predicting system for processing time-series data, it is very difficult to obtain a precise and reliable result by learning partial data.